where \(W_1\)  is the weight matrix of the first layer, and \(k < n\) . The function \(\sigma \)  is typically a non-linear activation function such as a sigmoid or a rectified linear unit (ReLU) [1]}. Another layer then maps \(y_i\)  to \(\hat{x_i} \in \mathbb {R}^{n\times 1}\)  according to
\(\hat{x_i} = \sigma (W_2y_i + b_2) = \sigma (W_2 \sigma (W_1x_i + b_1) +b_2)\) 
